Question

which set of ordered pairs represents a function? answer attempt 1 out of 2 \\(\\{(-5,-9),(-7,-9),(-5,-7),(-8,6)\\}\\) \\(\\{(-1,6),(0,-3),(5,-9),(-1,3)\\}\\) \\(\\{(1,2),(-6,2),(3,9),(5,3)\\}\\) \\(\\{(-3,9),(2,7),(2,-4),(1,5)\\}\\)

Explanation:

To determine if a set of ordered pairs represents a function, we use the definition of a function: each input (x - value) must have exactly one output (y - value). In other words, no two ordered pairs can have the same x - value with different y - values.

Step 1: Analyze the first set \(\{(-5,-9),(-7,-9),(-5,-7),(-8,6)\}\)

We look at the x - values: \(-5\), \(-7\), \(-5\), \(-8\). The x - value \(-5\) appears twice, with corresponding y - values \(-9\) and \(-7\). Since one input (\(-5\)) has two different outputs, this set does not represent a function.

Step 2: Analyze the second set \(\{(-1,6),(0,-3),(5,-9),(-1,3)\}\)

The x - values are \(-1\), \(0\), \(5\), \(-1\). The x - value \(-1\) appears twice, with corresponding y - values \(6\) and \(3\). Since one input (\(-1\)) has two different outputs, this set does not represent a function.

Step 3: Analyze the third set \(\{(1,2),(-6,2),(3,9),(5,3)\}\)

The x - values are \(1\), \(-6\), \(3\), \(5\). Each x - value appears only once. Even though the x - values \(1\) and \(-6\) have the same y - value (\(2\)), this is allowed in a function (multiple inputs can have the same output, but not the other way around). So this set represents a function.

Step 4: Analyze the fourth set \(\{(-3,9),(2,7),(2,-4),(1,5)\}\)

The x - values are \(-3\), \(2\), \(2\), \(1\). The x - value \(2\) appears twice, with corresponding y - values \(7\) and \(-4\). Since one input (\(2\)) has two different outputs, this set does not represent a function.

Answer:

\(\{(1,2),(-6,2),(3,9),(5,3)\}\)